Dirac operator on the sphere with attached wires

doi:10.1088/1674-1056/25/4/047303

Abstract

An explicitly solvable model for tunnelling of relativistic spinless particles through a sphere is suggested. The model operator is constructed by an operator extensions theory method from the orthogonal sum of the Dirac operators on a semi-axis and on the sphere. The transmission coefficient is obtained. The dependence of the transmission coefficient on the particle energy has a resonant character. One observes pairs of the Breit-Wigner and the Fano resonances. It correlates with the corresponding results for a non-relativistic particle.

Keywords: Dirac operator nanostructure tunnelling solvable model

Received: 08 July 2015
Revised: 09 January 2016
Accepted manuscript online:

PACS:	73.23.Ad	(Ballistic transport)
	73.63.-b	(Electronic transport in nanoscale materials and structures)
	02.30.Tb	(Operator theory)

Fund:

Project partially financially supported by the Funds from the Government of the Russian Federation (Grant No. 074-U01), the Funds from the Ministry of Education and Science of the Russian Federation (GOSZADANIE 2014/190) (Grant Nos. 14.Z50.31.0031 and 1.754.2014/K), and the President Foundation of the Russian Federation (Grant No. MK-5001.2015.1).

Corresponding Authors: I Yu Popov
E-mail: popov1955@gmail.com

Cite this article:

E N Grishanov, D A Eremin, D A Ivanov, I Yu Popov Dirac operator on the sphere with attached wires 2016 Chin. Phys. B 25 047303

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